Mick Philpott broke down in tears as he recalled before reporters his thwarted efforts to reach the children, who were sleeping in their beds in upstairs rooms when the fire began to rage in the early hours of Friday morning.
Five of the siblings were killed immediately in the central England city of Derby, while a sixth died in hospital Sunday as a result of his injuries.
Police confirmed that the fire broke out after fuel was poured through the mail box on the front door of the house, and said they plan to question Philpott and the children's mother to determine why the home may have been targeted.
"What I can tell you is that the fire was started deliberately," said Derbyshire police's Assistant Chief Constable Steve Cotterill.
He said that it would be "important that we talk to Mr. and Mrs. Philpott about what happened," but insisted they were being helped by police officers as they grieve.
Philpott had previously featured on British television in programs about his extraordinarily large family. In 2007, he hosted then-lawmaker Anne Widdicombe to live at his home for a week as she filmed a critical documentary about the country's welfare system.
Speaking at a news conference in Derby, Philpott offered thanks to members of the community who had supported his family since the blaze -- including an unnamed boy who tried to help him reach his children.
"There's a young lad who tried to get in the house, the same as myself," he said, describing the thwarted rescue attempt. "Then of course there is the four firemen, the police, the ambulances, the doctors and nurses -- everybody who tried to help save our children."
Jade, 10; John, 9; Jack, 7; Jessie, 6 and Jayden, 5, died at the scene from smoke inhalation. Their brother Duwayne, 13, died in the hospital on Sunday.
Two people arrested in the case were released without charge on Saturday.
Cotterill said he had asked residents living close to Philpott's home, in the working class Allenton district of Derby, to check their yards for containers that may have been used to carry the fuel poured into the family's house. He also appealed to local gas stations to check if they had sold fuel canisters in recent days.